David M. Solomon, tapped Tuesday as CEO, inherits a firm that survived the financial crisis and now needs to figure out how to grow

NEW YORK—Lloyd Blankfein secured the survival of Goldman Sachs Group Inc. by leading it through the financial crisis. The challenge for its next leader: how to thrive in a radically altered postcrisis world.

The bank on Tuesday said David M. Solomon, Goldman’s president and chief operating officer, will take over Oct. 1 as chief executive from Mr. Blankfein. The move puts a symbolic cap on Goldman’s postcrisis era and will fuel the firm’s continued evolution from a secretive trading powerhouse into a more nimble and entrepreneurial...